In this paper, we introduce a fuzzy extension of a class of measures for comparing clustering structures, namely measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast to previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure.
International audienceSimilarity measures aim at quantifying the extent to which objects resemble each other. Many techniques in data mining, data analysis or information retrieval require a similarity measure, and selecting an appropriate measure for a given problem is a difficult task. In this paper, the diverse forms similarity measures can take are examined, as well as their relationships and respective properties. Their semantic differences are highlighted and numerical tools to quantify these differences are proposed, considering several points of view and including global and local comparisons, order-based and value-based comparisons, and mathematical properties such as derivability. The paper studies similarity measures for two types of data: binary and numerical data, i.e., set data represented by the presence or absence of characteristics and data represented by real vectors
Gradual dependencies of the form the more A, the more B offer valuable information that linguistically express relationships between variations of the attributes. Several formalisations and automatic extraction algorithms have been proposed recently. In this paper, we first present an overview of these methods. We then propose an algorithm that combines the principles of several existing approaches and benefits from efficient computational properties to extract frequent gradual itemsets.
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